Question

The perimeter of a rectangular photograph is 22 inches. The length of the photograph is 1 inch more than the width. What are the dimensions of the photograph?

Short answer

The required dimensions of the rectangular photograph are: length = 6 inches and width = 5 inches

Step-by-step solution

Step-1 – Given

Given that the perimeter = 22 inches

The length is 1 inch more than its width.

Step-2 – To determine

We have to find the dimensions of the given rectangular photograph.

Step-3 – Calculation

Let the width = x inches
So, length = (x + 1) inches.

The equation of the perimeter would be,

$2[(x+1)+x]=22$

Then we solve the equation.

$\begin{array}{l}2[(x+1)+x]=22\\ 2(x+1+x)=22\\ 2(2x+1)=22\left[\text{combineliketerms}\right]\\ 4x+2=22\\ 4x+2-2=22-2\left[\text{subtract2foreachside}\right]\\ 4x=20\\ 4x÷4=20÷4\left[\text{divideeahsidewith4}\right]\\ x=5\\ length=x+1\\ length=5+1\left[\text{puttingvalueof}x\right]\\ length=6\\ \\ width=x\\ width=5\left[\text{puttingvalueof}x\right]\end{array}$

Hence, the dimensions of the rectangular photograph are: length = 6 inches and width = 5 inches.